We give a survey of Adrian Ioana-s cocycle superrigidity theorem for profinite actions of Property T groups and its applications to ergodic theory and set theory in this expository paper. In addition to a statement and proof of Ioana-s theorem, this paper features the following: i an introduction to rigidity, including a crash course in Borel cocycles and a summaryof some of the best-known superrigidity theorems; ii some easy applications of superrigidity, both to ergodic theory orbit equivalenceand set theory Borel reducibility; and iii a streamlined proof of Simon Thomas-s theorem that the classification of torsion-free abelian groups of finite rank is intractable.